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AbstractRegion (Commons Math 3.2 API)
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org.apache.commons.math3.geometry.partitioning</FONT>
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Class AbstractRegion&lt;S extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>,T extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.geometry.partitioning.AbstractRegion&lt;S,T&gt;</B>
</PRE>
<DL>
<DT><DT><B>Type Parameters:</B><DD><CODE>S</CODE> - Type of the space.<DD><CODE>T</CODE> - Type of the sub-space.</DL>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;S&gt;</DD>
</DL>
<DL>
<DT><B>Direct Known Subclasses:</B> <DD><A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/oned/IntervalsSet.html" title="class in org.apache.commons.math3.geometry.euclidean.oned">IntervalsSet</A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">PolygonsSet</A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/euclidean/threed/PolyhedronsSet.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">PolyhedronsSet</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public abstract class <B>AbstractRegion&lt;S extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>,T extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;S&gt;</DL>
</PRE>

<P>
Abstract class for all regions, independently of geometry type or dimension.
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: AbstractRegion.java 1416643 2012-12-03 19:37:14Z tn $</DD>
</DL>
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&nbsp;<A NAME="nested_classes_inherited_from_class_org.apache.commons.math3.geometry.partitioning.Region"><!-- --></A>
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<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Nested classes/interfaces inherited from interface org.apache.commons.math3.geometry.partitioning.<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html" title="enum in org.apache.commons.math3.geometry.partitioning">Region.Location</A></CODE></TD>
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<CODE>protected </CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#AbstractRegion()">AbstractRegion</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a region representing the whole space.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected </CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#AbstractRegion(org.apache.commons.math3.geometry.partitioning.BSPTree)">AbstractRegion</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;tree)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a region from an inside/outside BSP tree.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected </CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#AbstractRegion(java.util.Collection)">AbstractRegion</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&gt;&nbsp;boundary)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a Region from a Boundary REPresentation (B-rep).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#AbstractRegion(org.apache.commons.math3.geometry.partitioning.Hyperplane[])">AbstractRegion</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Hyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">Hyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;[]&nbsp;hyperplanes)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a convex region from an array of bounding hyperplanes.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

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<B>Method Summary</B></FONT></TH>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#applyTransform(org.apache.commons.math3.geometry.partitioning.Transform)">applyTransform</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Transform.html" title="interface in org.apache.commons.math3.geometry.partitioning">Transform</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt;&nbsp;transform)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transform a region.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>abstract &nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#buildNew(org.apache.commons.math3.geometry.partitioning.BSPTree)">buildNew</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;newTree)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a region using the instance as a prototype.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html" title="enum in org.apache.commons.math3.geometry.partitioning">Region.Location</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#checkPoint(org.apache.commons.math3.geometry.partitioning.BSPTree, org.apache.commons.math3.geometry.Vector)">checkPoint</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;node,
           <A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;point)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check a point with respect to the region starting at a given node.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html" title="enum in org.apache.commons.math3.geometry.partitioning">Region.Location</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#checkPoint(org.apache.commons.math3.geometry.Vector)">checkPoint</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;point)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check a point with respect to the region.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected abstract &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#computeGeometricalProperties()">computeGeometricalProperties</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute some geometrical properties.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#contains(org.apache.commons.math3.geometry.partitioning.Region)">contains</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;region)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if the instance entirely contains another region.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#copySelf()">copySelf</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Copy the instance.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getBarycenter()">getBarycenter</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the barycenter of the instance.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getBoundarySize()">getBoundarySize</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the size of the boundary.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getSize()">getSize</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the size of the instance.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getTree(boolean)">getTree</A></B>(boolean&nbsp;includeBoundaryAttributes)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the underlying BSP tree.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#intersection(org.apache.commons.math3.geometry.partitioning.SubHyperplane)">intersection</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;sub)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the parts of a sub-hyperplane that are contained in the region.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#isEmpty()">isEmpty</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if the instance is empty.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#isEmpty(org.apache.commons.math3.geometry.partitioning.BSPTree)">isEmpty</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;node)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if the sub-tree starting at a given node is empty.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#setBarycenter(org.apache.commons.math3.geometry.Vector)">setBarycenter</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;barycenter)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Set the barycenter of the instance.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#setSize(double)">setSize</A></B>(double&nbsp;size)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Set the size of the instance.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Side.html" title="enum in org.apache.commons.math3.geometry.partitioning">Side</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#side(org.apache.commons.math3.geometry.partitioning.Hyperplane)">side</A></B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Hyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">Hyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;hyperplane)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the relative position of the instance with respect to an
 hyperplane.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
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<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ========= CONSTRUCTOR DETAIL ======== -->

<A NAME="constructor_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Constructor Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="AbstractRegion()"><!-- --></A><H3>
AbstractRegion</H3>
<PRE>
protected <B>AbstractRegion</B>()</PRE>
<DL>
<DD>Build a region representing the whole space.
<P>
</DL>
<HR>

<A NAME="AbstractRegion(org.apache.commons.math3.geometry.partitioning.BSPTree)"><!-- --></A><H3>
AbstractRegion</H3>
<PRE>
protected <B>AbstractRegion</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;tree)</PRE>
<DL>
<DD>Build a region from an inside/outside BSP tree.
 <p>The leaf nodes of the BSP tree <em>must</em> have a
 <code>Boolean</code> attribute representing the inside status of
 the corresponding cell (true for inside cells, false for outside
 cells). In order to avoid building too many small objects, it is
 recommended to use the predefined constants
 <code>Boolean.TRUE</code> and <code>Boolean.FALSE</code>. The
 tree also <em>must</em> have either null internal nodes or
 internal nodes representing the boundary as specified in the
 <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getTree(boolean)"><CODE>getTree</CODE></A> method).</p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>tree</CODE> - inside/outside BSP tree representing the region</DL>
</DL>
<HR>

<A NAME="AbstractRegion(java.util.Collection)"><!-- --></A><H3>
AbstractRegion</H3>
<PRE>
protected <B>AbstractRegion</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&gt;&nbsp;boundary)</PRE>
<DL>
<DD>Build a Region from a Boundary REPresentation (B-rep).
 <p>The boundary is provided as a collection of <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>sub-hyperplanes</CODE></A>. Each sub-hyperplane has the
 interior part of the region on its minus side and the exterior on
 its plus side.</p>
 <p>The boundary elements can be in any order, and can form
 several non-connected sets (like for example polygons with holes
 or a set of disjoints polyhedrons considered as a whole). In
 fact, the elements do not even need to be connected together
 (their topological connections are not used here). However, if the
 boundary does not really separate an inside open from an outside
 open (open having here its topological meaning), then subsequent
 calls to the <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#checkPoint(org.apache.commons.math3.geometry.Vector)"><CODE>checkPoint</CODE></A> method will not be
 meaningful anymore.</p>
 <p>If the boundary is empty, the region will represent the whole
 space.</p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>boundary</CODE> - collection of boundary elements, as a
 collection of <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>SubHyperplane</CODE></A> objects</DL>
</DL>
<HR>

<A NAME="AbstractRegion(org.apache.commons.math3.geometry.partitioning.Hyperplane[])"><!-- --></A><H3>
AbstractRegion</H3>
<PRE>
public <B>AbstractRegion</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Hyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">Hyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;[]&nbsp;hyperplanes)</PRE>
<DL>
<DD>Build a convex region from an array of bounding hyperplanes.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>hyperplanes</CODE> - array of bounding hyperplanes (if null, an
 empty region will be built)</DL>
</DL>

<!-- ============ METHOD DETAIL ========== -->

<A NAME="method_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Method Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="buildNew(org.apache.commons.math3.geometry.partitioning.BSPTree)"><!-- --></A><H3>
buildNew</H3>
<PRE>
public abstract <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt; <B>buildNew</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;newTree)</PRE>
<DL>
<DD>Build a region using the instance as a prototype.
 <p>This method allow to create new instances without knowing
 exactly the type of the region. It is an application of the
 prototype design pattern.</p>
 <p>The leaf nodes of the BSP tree <em>must</em> have a
 <code>Boolean</code> attribute representing the inside status of
 the corresponding cell (true for inside cells, false for outside
 cells). In order to avoid building too many small objects, it is
 recommended to use the predefined constants
 <code>Boolean.TRUE</code> and <code>Boolean.FALSE</code>. The
 tree also <em>must</em> have either null internal nodes or
 internal nodes representing the boundary as specified in the
 <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#getTree(boolean)"><CODE>getTree</CODE></A> method).</p>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#buildNew(org.apache.commons.math3.geometry.partitioning.BSPTree)">buildNew</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>newTree</CODE> - inside/outside BSP tree representing the new region
<DT><B>Returns:</B><DD>the built region</DL>
</DD>
</DL>
<HR>

<A NAME="copySelf()"><!-- --></A><H3>
copySelf</H3>
<PRE>
public <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt; <B>copySelf</B>()</PRE>
<DL>
<DD>Copy the instance.
 <p>The instance created is completely independant of the original
 one. A deep copy is used, none of the underlying objects are
 shared (except for the underlying tree <code>Boolean</code>
 attributes and immutable objects).</p>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#copySelf()">copySelf</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>a new region, copy of the instance</DL>
</DD>
</DL>
<HR>

<A NAME="isEmpty()"><!-- --></A><H3>
isEmpty</H3>
<PRE>
public boolean <B>isEmpty</B>()</PRE>
<DL>
<DD>Check if the instance is empty.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#isEmpty()">isEmpty</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>true if the instance is empty</DL>
</DD>
</DL>
<HR>

<A NAME="isEmpty(org.apache.commons.math3.geometry.partitioning.BSPTree)"><!-- --></A><H3>
isEmpty</H3>
<PRE>
public boolean <B>isEmpty</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;node)</PRE>
<DL>
<DD>Check if the sub-tree starting at a given node is empty.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#isEmpty(org.apache.commons.math3.geometry.partitioning.BSPTree)">isEmpty</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>node</CODE> - root node of the sub-tree (<em>must</em> have <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>Region</CODE></A> tree semantics, i.e. the leaf nodes must have
 <code>Boolean</code> attributes representing an inside/outside
 property)
<DT><B>Returns:</B><DD>true if the sub-tree starting at the given node is empty</DL>
</DD>
</DL>
<HR>

<A NAME="contains(org.apache.commons.math3.geometry.partitioning.Region)"><!-- --></A><H3>
contains</H3>
<PRE>
public boolean <B>contains</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;region)</PRE>
<DL>
<DD>Check if the instance entirely contains another region.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#contains(org.apache.commons.math3.geometry.partitioning.Region)">contains</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>region</CODE> - region to check against the instance
<DT><B>Returns:</B><DD>true if the instance contains the specified tree</DL>
</DD>
</DL>
<HR>

<A NAME="checkPoint(org.apache.commons.math3.geometry.Vector)"><!-- --></A><H3>
checkPoint</H3>
<PRE>
public <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html" title="enum in org.apache.commons.math3.geometry.partitioning">Region.Location</A> <B>checkPoint</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;point)</PRE>
<DL>
<DD>Check a point with respect to the region.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#checkPoint(org.apache.commons.math3.geometry.Vector)">checkPoint</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>point</CODE> - point to check
<DT><B>Returns:</B><DD>a code representing the point status: either <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html#INSIDE"><CODE>Region.Location.INSIDE</CODE></A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html#OUTSIDE"><CODE>Region.Location.OUTSIDE</CODE></A> or <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html#BOUNDARY"><CODE>Region.Location.BOUNDARY</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="checkPoint(org.apache.commons.math3.geometry.partitioning.BSPTree, org.apache.commons.math3.geometry.Vector)"><!-- --></A><H3>
checkPoint</H3>
<PRE>
protected <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html" title="enum in org.apache.commons.math3.geometry.partitioning">Region.Location</A> <B>checkPoint</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;node,
                                     <A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;point)</PRE>
<DL>
<DD>Check a point with respect to the region starting at a given node.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>node</CODE> - root node of the region<DD><CODE>point</CODE> - point to check
<DT><B>Returns:</B><DD>a code representing the point status: either <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html#INSIDE"><CODE>INSIDE</CODE></A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html#OUTSIDE"><CODE>OUTSIDE</CODE></A> or <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html#BOUNDARY"><CODE>BOUNDARY</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="getTree(boolean)"><!-- --></A><H3>
getTree</H3>
<PRE>
public <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt; <B>getTree</B>(boolean&nbsp;includeBoundaryAttributes)</PRE>
<DL>
<DD>Get the underlying BSP tree.

 <p>Regions are represented by an underlying inside/outside BSP
 tree whose leaf attributes are <code>Boolean</code> instances
 representing inside leaf cells if the attribute value is
 <code>true</code> and outside leaf cells if the attribute is
 <code>false</code>. These leaf attributes are always present and
 guaranteed to be non null.</p>

 <p>In addition to the leaf attributes, the internal nodes which
 correspond to cells split by cut sub-hyperplanes may contain
 <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BoundaryAttribute.html" title="class in org.apache.commons.math3.geometry.partitioning"><CODE>BoundaryAttribute</CODE></A> objects representing
 the parts of the corresponding cut sub-hyperplane that belong to
 the boundary. When the boundary attributes have been computed,
 all internal nodes are guaranteed to have non-null
 attributes, however some <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BoundaryAttribute.html" title="class in org.apache.commons.math3.geometry.partitioning"><CODE>BoundaryAttribute</CODE></A> instances may have their <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BoundaryAttribute.html#plusInside"><CODE>plusInside</CODE></A> and <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BoundaryAttribute.html#plusOutside"><CODE>plusOutside</CODE></A> fields both null if
 the corresponding cut sub-hyperplane does not have any parts
 belonging to the boundary.</p>

 <p>Since computing the boundary is not always required and can be
 time-consuming for large trees, these internal nodes attributes
 are computed using lazy evaluation only when required by setting
 the <code>includeBoundaryAttributes</code> argument to
 <code>true</code>. Once computed, these attributes remain in the
 tree, which implies that in this case, further calls to the
 method for the same region will always include these attributes
 regardless of the value of the
 <code>includeBoundaryAttributes</code> argument.</p>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#getTree(boolean)">getTree</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>includeBoundaryAttributes</CODE> - if true, the boundary attributes
 at internal nodes are guaranteed to be included (they may be
 included even if the argument is false, if they have already been
 computed due to a previous call)
<DT><B>Returns:</B><DD>underlying BSP tree<DT><B>See Also:</B><DD><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/BoundaryAttribute.html" title="class in org.apache.commons.math3.geometry.partitioning"><CODE>BoundaryAttribute</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="getBoundarySize()"><!-- --></A><H3>
getBoundarySize</H3>
<PRE>
public double <B>getBoundarySize</B>()</PRE>
<DL>
<DD>Get the size of the boundary.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#getBoundarySize()">getBoundarySize</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the size of the boundary (this is 0 in 1D, a length in
 2D, an area in 3D ...)</DL>
</DD>
</DL>
<HR>

<A NAME="getSize()"><!-- --></A><H3>
getSize</H3>
<PRE>
public double <B>getSize</B>()</PRE>
<DL>
<DD>Get the size of the instance.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#getSize()">getSize</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the size of the instance (this is a length in 1D, an area
 in 2D, a volume in 3D ...)</DL>
</DD>
</DL>
<HR>

<A NAME="setSize(double)"><!-- --></A><H3>
setSize</H3>
<PRE>
protected void <B>setSize</B>(double&nbsp;size)</PRE>
<DL>
<DD>Set the size of the instance.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>size</CODE> - size of the instance</DL>
</DD>
</DL>
<HR>

<A NAME="getBarycenter()"><!-- --></A><H3>
getBarycenter</H3>
<PRE>
public <A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt; <B>getBarycenter</B>()</PRE>
<DL>
<DD>Get the barycenter of the instance.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#getBarycenter()">getBarycenter</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>an object representing the barycenter</DL>
</DD>
</DL>
<HR>

<A NAME="setBarycenter(org.apache.commons.math3.geometry.Vector)"><!-- --></A><H3>
setBarycenter</H3>
<PRE>
protected void <B>setBarycenter</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/Vector.html" title="interface in org.apache.commons.math3.geometry">Vector</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;barycenter)</PRE>
<DL>
<DD>Set the barycenter of the instance.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>barycenter</CODE> - barycenter of the instance</DL>
</DD>
</DL>
<HR>

<A NAME="computeGeometricalProperties()"><!-- --></A><H3>
computeGeometricalProperties</H3>
<PRE>
protected abstract void <B>computeGeometricalProperties</B>()</PRE>
<DL>
<DD>Compute some geometrical properties.
 <p>The properties to compute are the barycenter and the size.</p>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="side(org.apache.commons.math3.geometry.partitioning.Hyperplane)"><!-- --></A><H3>
side</H3>
<PRE>
public <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Side.html" title="enum in org.apache.commons.math3.geometry.partitioning">Side</A> <B>side</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Hyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">Hyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;hyperplane)</PRE>
<DL>
<DD>Compute the relative position of the instance with respect to an
 hyperplane.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#side(org.apache.commons.math3.geometry.partitioning.Hyperplane)">side</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>hyperplane</CODE> - reference hyperplane
<DT><B>Returns:</B><DD>one of <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Side.html#PLUS"><CODE>Side.PLUS</CODE></A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Side.html#MINUS"><CODE>Side.MINUS</CODE></A>, <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Side.html#BOTH"><CODE>Side.BOTH</CODE></A> or <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Side.html#HYPER"><CODE>Side.HYPER</CODE></A> (the latter result can occur only if the tree
 contains only one cut hyperplane)</DL>
</DD>
</DL>
<HR>

<A NAME="intersection(org.apache.commons.math3.geometry.partitioning.SubHyperplane)"><!-- --></A><H3>
intersection</H3>
<PRE>
public <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt; <B>intersection</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>&gt;&nbsp;sub)</PRE>
<DL>
<DD>Get the parts of a sub-hyperplane that are contained in the region.
 <p>The parts of the sub-hyperplane that belong to the boundary are
 <em>not</em> included in the resulting parts.</p>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#intersection(org.apache.commons.math3.geometry.partitioning.SubHyperplane)">intersection</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A> extends <A HREF="../../../../../../org/apache/commons/math3/geometry/Space.html" title="interface in org.apache.commons.math3.geometry">Space</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>sub</CODE> - sub-hyperplane traversing the region
<DT><B>Returns:</B><DD>filtered sub-hyperplane</DL>
</DD>
</DL>
<HR>

<A NAME="applyTransform(org.apache.commons.math3.geometry.partitioning.Transform)"><!-- --></A><H3>
applyTransform</H3>
<PRE>
public <A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt; <B>applyTransform</B>(<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/Transform.html" title="interface in org.apache.commons.math3.geometry.partitioning">Transform</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">S</A>,<A HREF="../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="type parameter in AbstractRegion">T</A>&gt;&nbsp;transform)</PRE>
<DL>
<DD>Transform a region.
 <p>Applying a transform to a region consist in applying the
 transform to all the hyperplanes of the underlying BSP tree and
 of the boundary (and also to the sub-hyperplanes embedded in
 these hyperplanes) and to the barycenter. The instance is not
 modified, a new instance is built.</p>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>transform</CODE> - transform to apply
<DT><B>Returns:</B><DD>a new region, resulting from the application of the
 transform to the instance</DL>
</DD>
</DL>
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